Season 2 • Episode 05 • Venn diagrams
0Venn diagrams
Season 2
Episode 05 Time frame 1 period
Prerequisites :
Objectives :
•
See examples of Venn diagrams.•
Review the main set operations.Materials :
•
Lesson about Venn diagrams.•
Mathing ards with denitions and Venn diagrams.1 – Matching game with sets definitions and diagrams 10 mins
Eighteen denitions and eighteen Venn diagrams are handed out to the students. They
mingle tond the rightdiagramfor their denition and vie-versa..
2 – Oral presentations 45 mins
After a few lesson slides, eah pair of students goes to the board to explain the diagram
and the denition. Alldiagramsare inluded in the beamer.
Venn diagrams
Season 2
Episode 05 Document Lesson
Venndiagramsare graphialrepresentationsof relationsbetween two,threeormoresets.
Eah set is represented by a simple geometrial shape, suh as a irle, an ellipse or a
retangle.
One set inside a universe
In thisrst example,wesee the universe
Ω
(the inside of the retangle) and one sub-
set of
Ω
,A
(the inside of the irle). Theomplement of
A
inΩ
,A
,isthepart oftheretangle that is not inside the irle.
Ω A
A
Two sets inside a universe
Inthis seondexample,weseetheuniverse
Ω
and two subsets ofΩ
,A
(blak, on theright)and
B
(grey, onthe left).The inter-setion
A ∩ B
of the two sets is their om-mon part.Theunion
A ∪ B
ofthe twosetsistheinsideofthetwoirles,inludingthe
intersetion.
Ω A
B
Three sets inside a universe
Inthisthirdexample,weseetheuniverse
Ω
andthreesubsetsof
Ω
,A
(blak,ontheup-perright),
B
(grey, on the upper left) andC
(dashed, belowA
andB
). Every pos-sible intersetion or union of two or three
ofthesesetsandtheiromplementisrepre-
sentedonthisdiagram.Forexample,region
3is
(A ∩ B) ∩ C
,while(A ∪ B) ∩ C
ismadeΩ A
B
C 1
2 3
4 5
6
7
8
Venn diagrams
Season 2
Episode 05 Document Solutions
Realnumbers that are not deimal. Realnumbers that are deimal.
Parallelograms with their diagonals
equalorperpendiular.
Parallelograms with their diagonals
equaland perpendiular.
Integersmultiplesof 7andof2but not Integers multiples of 7 that are not
Season 2 • Episode 05 • Venn diagrams
3Naturalnumbers that are neithermul-
tiple of 2nor multiplesof 3.
Parallelogramswiththeirdiagonalsnot
equalorperpendiular.
Parallelograms with their diagonals
equal or perpendiular or neither but
not both.
Parallelograms with their diagonals
equaland perpendiular or neither.
Inthesetofrealnumbers,naturalnum-
bers and irrationalnumbers.
Real numbers that are neither irratio-
nalnor natural.
Season 2 • Episode 05 • Venn diagrams
4Irrationaland deimal real numbers.
Isoseles triangles that are not equila-
teral.
Trigonometri and linear funtions
suh that
f (0) = 0
.Funtions suh that
f (0) = 0
that areneitherlinear nor trigonometri.
Funtions suh that
f (0) 6= 0
that areneither linear nor trigonometri.
All linear and trigonometri funtions
andotherfuntionssuhthat
f (0) 6= 0
.Season 2 • Episode 05 • Venn diagrams
5Document 1
Mathing ards : denitions and Venn DiagramsRealnumbers that are not deimal.
Realnumbers that are deimal.
Parallelogramswith their diagonalsequal orperpendiular.
Parallelogramswith their diagonalsequaland perpendiular.
Integers multiples of 7and of 2but not of 14.
Integers multiples of 7that are not even.
Isoseles trianglesthat are not equilateral.
In the set of real numbers, naturalnumbers and irrationalnumbers.
Natural numbers that are neither multipleof 2nor multiplesof 3.
Parallelograms with their diagonalsnot equalor perpendiular.
Parallelograms with their diagonalsequaland perpendiular or neither.
Parallelogramswith their diagonals equalorperpendiular or neitherbut not both.
Irrational and deimalreal numbers.
Real numbers that are neitherirrationalnor natural.
Trigonometri and linear funtions suh that
f (0) = 0
.Funtions suh that
f (0) = 0
that are neitherlinear nor trigonometri.Funtions suh that
f (0) 6= 0
that are neitherlinear nor trigonometri.All linear and trigonometrifuntions and other funtions suh that
